The strong global dimension of piecewise hereditary algebras

Let T be a tilting object in a triangulated category which is equivalent to the bounded derived category of a finite-dimensional hereditary algebra. The text investigages the strong global dimension, in the sense of Ringel, of the opposite algebra A of the endomorphism algebra of T . This invariant is expressed in terms of the lengths of the sequences T0, . . . , Tl of tilting objects such that Tl = T , each term arises from the preceding one by a tilting mutation, and the opposite of the endomorphism algebra of T0 is a tilted algebra. It is also expressed in terms on the hereditary abelian subcategories of the triangulated category.